Nucleophilicity from a Conceptual DFT Viewpoint: A Four-State Ensemble-Inspired Model

By taking advantage of the fundamental convexity of the exact energy as a function of the number of electrons, we extrapolate the straight-line segments connecting the N and N + 1 states and N – 2 and N – 1 states in a four-state ensemble-inspired model. These segments intersect at a unique point that determines a fractional charge transfer condition,ΔNint−=−λ, which naturally contemplates the reactivity of the cation and neutral forms in terms of their hardness. The energy evaluated at the intersection point, Ni, and the energy evaluated at −λ in the ensemble segment,Nl, give rise to our proposed descriptors that contribute to the electronic panorama of the donation process and describe the reactivity of a set of molecules in specific conditions. The performance of the indicators as nucleophilic indices was evaluated in five chemical reactions: the oxidation of metals, the proton affinity of amines, the stability of coordinated metals that follow the Irving–Williams series, and the kinetic substitution of indoles and alkenes. The nucleophilicity indices proposed are an important complement to the electrophilicity index because they are based on a different response that, although they may lead to similar results with respect to the correlation with a given property, they may be used to recognize dominant aspects of the electronic structure in a chemical interaction. The results obtained support their use as complementary descriptors of the intrinsic electronic contribution to nucleophilic reactivity within specified reaction families.